Visualising and representing

  • Dicey
    problem

    Dicey

    Age
    7 to 11
    Challenge level
    A game has a special dice with a colour spot on each face. These three pictures show different views of the same dice. What colour is opposite blue?
  • Knight's Swap
    problem

    Knight's Swap

    Age
    7 to 11
    Challenge level
    Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?
  • Midpoint Triangle
    problem

    Midpoint Triangle

    Age
    7 to 11
    Challenge level
    Can you cut up a square in the way shown and make the pieces into a triangle?
  • A Flying Holiday
    problem

    A Flying Holiday

    Age
    7 to 11
    Challenge level
    Follow the journey taken by this bird and let us know for how long and in what direction it must fly to return to its starting point.
  • Colour Wheels
    problem

    Colour Wheels

    Age
    7 to 11
    Challenge level

    Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

  • Paw Prints
    problem

    Paw Prints

    Age
    7 to 11
    Challenge level
    A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?
  • Painted Faces
    problem

    Painted Faces

    Age
    7 to 11
    Challenge level
    Imagine a 3 by 3 by 3 cube made of 9 small cubes. Each face of the large cube is painted a different colour. How many small cubes will have two painted faces? Where are they?
  • More Building with Cubes
    problem

    More Building With Cubes

    Age
    7 to 11
    Challenge level
    Here are more buildings to picture in your mind's eye. Watch out - they become quite complicated!
  • Reef and Granny
    problem

    Reef and Granny

    Age
    7 to 11
    Challenge level

    Have a look at what happens when you pull a reef knot and a granny knot tight. Which do you think is best for securing things together? Why?

  • Putting Two and Two Together
    problem

    Putting Two and Two Together

    Age
    7 to 11
    Challenge level
    In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?
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